Dubious Logic

More equal than others

I left you pondering a card combination at the end of last week's article - how to play this suit for five tricks:

You quite reasonably might have suspected a trap as earlier I considered Q4 opposite AK1093 and discovered that the best technique was to play the suit from the top. Indeed, this holding is different but yields to the same analysis. If we play ace, king, queen we will be successful whenever they are 3-3 and that's that; twenty possibilities in all. No short holding of the missing honour helps us as even though J8 might fall in the first two rounds, as a defender holding the lowly seven will take a trick.

The alternative is to run the ten immediately. That wins half the 3-3 breaks - when the knave is onside - so ten cancel out - but loses the other half. Considering the 4-2 divisions, the finesse wins when there is either Jx or Jxxx onside. That's a healthy 15 additional combinations and running ten is seen to be the better play.

What happens if you do all these calculations and find that the answer is a tie? Well you could flip a coin but perhaps now is the time to consider the relative frequencies of each division. This hand, which has every appearance of a problem, arose in a recent early round of Crockfords:

I opened an artificial 2♣ intending to rebid in no-trumps describing a balanced 23-24 HCP. Over my partner's inevitable 2♦ negative, my right hand opponent bid 2♠ and after an uncertain auction, I found myself in 3NT. North led his partner's suit and I held up to the third round discovering that South had seven spades and North just one (he threw a heart then a diamond). As South had lots of winners, I had no chance if he also had the club ace, so with that in mind, how then to play that suit?

Curiously I could afford to lose two club tricks: say I played a club to the queen and led one back with South showing out. North would be welcome to his ace and knave but would then have to lead a red card into my AKJ holdings. I would get an extra trick there, three clubs, a spade and my two ace-kings for nine. All sound except for one instance. If North had all four clubs, he could afford to give me a trick because he could stop me scoring dummy's long card by retaining a winner until the fourth round.

I could prevent this by leading the king on the first round. Now I would see South show out and I could finesse against North's club knave. He would do well to hold up the ace and restrict me to three tricks. But again, having to lead a red card would be his undoing. However there was one thing to be said against this: North might hold a singleton ace and playing the king from hand would promote South's knave as an entry.

It was one against one. It seemed clear to me that North, who had twelve 'non-spades' was much more likely to have length than South who had only six spaces. It would have been a shame after all this cerebration not to back my judgement and I duly played the club king from hand. I expect you can guess what happened – North really did have a 1=6=5=1 hand with the singleton club ace. For my own peace of mind I had to look up the percentages: 4-0 with the spades 1-7 was over 16%, the exact 1-3, under 2%. It's one of the attractions of bridge: you get taught the occasional life lesson along the way.

Published Saturday 11.Feb.2006